Details

sample359.0ms

Algorithm

intervals

Results

177.0ms	77×	body	1280	valid
73.0ms	65×	body	640	valid
20.0ms	23×	body	320	valid
19.0ms	77×	body	80	valid
6.0ms	14×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2046
7	2046
6	911
5	367
4	177
3	95
2	61
1	25
0	13

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
12.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
29.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series763.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(hypot (sin ky) (sin kx))
247.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
326.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	2001
3	2001
2	1003
1	305
0	133

prune606.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.1b

localize44.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
0.2b	(* (sin th) (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
7×	`associate-r`
6×	`times-frac` `div-exp`
5×	`pow1` `cbrt-unprod`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`1-exp` `div-inv`
1×	`hypot-udef` `clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `associate-r/` `*-commutative` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
15.0ms	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
42.0ms	(* (sin th) (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))))

series782.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms	(hypot (sin ky) (sin kx))
260.0ms	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
367.0ms	(* (sin th) (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))))

simplify1.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	2000
3	2000
2	1123
1	323
0	132

prune509.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

13.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.6s

Counts

4 → 12

Calls

4 calls:

287.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
306.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
298.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
755.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.3s

Counts

168 → 168

Iterations

Iter	Nodes
done	2002
4	2002
3	1618
2	713
1	325
0	173

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))
8.0ms	(cbrt (sin ky))
3.0ms	(cbrt (sin ky))

series576.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (sin ky))
131.0ms	(cbrt (sin ky))
144.0ms	(cbrt (sin ky))
129.0ms	(cbrt (sin ky))

simplify942.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	2000
5	2000
4	1008
3	380
2	157
1	69
0	33

prune633.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.1b

regimes1.2s

Accuracy

0% (0.6b remaining)

Error of 9.4b against oracle of 8.8b and baseline of 9.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample12.0s

Algorithm

intervals

Results

6.3s	2666×	body	1280	valid
3.6s	1855×	body	640	valid
906.0ms	2336×	body	80	valid
763.0ms	787×	body	320	valid
244.0ms	356×	body	160	valid